Derived metrics
dTVL, emission efficiency, durability-adjusted yield and portfolio horizon — everything that follows from the attestation.
Argued in full in the whitepaper at §10.
dTVL#
Discount liquidity by its expected persistence relative to a reference duration:
dTVL_P = L_P · min( 1, H_P / H_ref )^ψ · c_P| Pool | TVL | Horizon | Confidence | dTVL |
|---|---|---|---|---|
| A | $500M | 9 days | 0.7 | $35M |
| B | $500M | 90 days | 0.7 | $350M |
Aggregated across a chain, the sum behaves very differently from headline TVL during an incentive programme — rising with organic deposits, flat or falling as subsidised deposits accumulate against a fixed expiry date. Two diverging lines on one chart is the most legible output the system has, and it needs no integration to consume.
Emission efficiency#
Programmes are usually judged on TVL acquired per dollar spent, which rewards buying liquidity that leaves the moment payment stops. The durability-aware version measures durable liquidity-days:
η_c = ∫ ( dTVL_P(t) − dTVL_P(t₀) ) dt / Σ R_P(t)Durability-adjusted yield#
An advertised APY assumes the position can be held. For a strategy requiring duration d:
APY_dur(d) = APY_P · S_P(d) − ( 1 − S_P(d) ) · χ_PThe second term is what every yield comparison leaves out. A breach is not merely the absence of yield — it is a realised loss taken at the worst moment, when everyone is exiting the same door. Run it and a 40% APY pool with a four-day horizon, held for thirty days, frequently prices below a 6% APY pool with a two-year horizon.
Portfolio horizon#
The minimum horizon across positions is too conservative — a small position breaching is survivable. The weighted mean is too permissive, because breaches correlate. So the joint survival is computed directly, with a Gaussian copula over the marginals and correlation from the cross-pool feature, and reported alongside:
n_eff = 1 / Σᵢ w̃ᵢ²